Question

Find the sum of the first 12 terms of the sequence. Show all work for full credit.

1, -4, -9, -14, . . .

Answer 1

well formula for finding the nth term is :-
\[\large \bf a_n=a+(n-1)d\]
where
a=first terms
n=no of that term
d=common difference

Answer 2

So the first term would be 1?

Answer 3

I don't know how to find the commons difference

Answer 4

common difference is difference between any two consecutive terms

Answer 5

so here common difference would be
-4-1=-5

Answer 6

got it ?

Answer 7

Ohhh okay yes I got it

Answer 8

good

Answer 9

so
\[\large \bf a_{12}=1+(12-1)(-5)\]

Answer 10

find 12th term ?

Answer 11

Okay hang on

Answer 12

I got -54

Answer 13

correct

Answer 14

so in previous question, i told you the formula if we have first term and last term ,we would surely use it now

Answer 15

remember that formula ?

Answer 16

Hang on

Answer 17

I can't remember what it was, I'm sorry

Answer 18

okay, np
here is the formula :-
\[\large \bf S_n=\frac{n}{2}(a+l)\]

Answer 19

can you tell me what is the value of n,a and l here ?

Answer 20

Is a still 1?

Answer 21

yep

Answer 22

And if we found the 12th term does n change? Or does one of them change to -54?

Answer 23

Or is n still 12?

Answer 24

Sorry for all the questions in just trying to understand

Answer 25

yep! n=12 i.e no of terms

Answer 26

and l=-54 i.e last terms

Answer 27

*term

Answer 28

Okay thank you

Answer 29

just plug all the values in given equation and solve

Answer 30

Okay

Answer 31

12

Answer 32

how ?

Answer 33

I'm not sure I think I did it wrong

Answer 34

haha you did

Answer 35

What do I do now?

Answer 36

\[\large \bf S_{12}=\frac{12}{2}(1-54)\]

Answer 37

solve it

Answer 38

OHHH. I forgot the 54

Answer 39

-318

Answer 40

correct

Answer 41

Okay what now? Or did I just finish it??

Answer 42

haha yes

Answer 43

Thank you so much!

Answer 44

np